Related papers: Schottky's theorem in $\mathbb{C}^n$

The purpose of this paper is to present a generalization of Forelli's theorem. In particular, we prove an all dimensional version of the two-dimensional theorem of Chirka of 2005.

A new proof of Oka's lemma is given for smoothly bounded, pseudoconvex domains $D\subset\mathbb{C}^n$. The method of proof is then also applied to other convexity-like hypotheses on the boundary of $D$.

We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.

In this work we present a simplifyed proof of Kantorovich's Theorem on Newton's Method. This analysis uses a technique which has already been used for obtaining new extensions of this theorem.

We state and prove a Lemma in 1 variable Calculus, that justifies some arguments previously used to ilustrate non-uniqueness of some generalized physical quantities.

In an earlier paper, we gave an abstract formulation of a theorem of Sierpi\'nski in uncountable commutative groups. In this paper, we prove a result which generalizes the earlier formulation.

Doob's theorem provides guarantees of consistent estimation and posterior consistency under very general conditions. Despite the limitation that it only guarantees consistency on a set with prior probability 1, for many models arising in…

In the paper we propose certain conditions, relatively easy to verify, which ensure the central limit theorem for some general class of Markov chains. To justify the usefulness of our criterion, we further verify it for a particular…

We prove that the "generic condition" used in singularity theorems of general relativity is generic in the space of Lorentzian metrics on a given manifold, in the sense that it is satisfied for all metrics in a residual set in the Whitney…

In this note we provide a new proof of the Tikhonov theorem for the infinite time interval and discuss some of its applications.

Schottky Conjecture is analytically proved for multi-stage field emitters consisting on the superposition of rectangular or trapezoidal protrusions on a line under some specific limit. The case in which a triangular protrusion is present on…

In this note we provide a quick proof of the Sklar's Theorem on the existence of copulas by using the generalized inverse functions as in the one dimensional case, but a little more sophisticated.

Based on various strategies and a new general doubling operator, we obtain several simple proofs of the celebrated Sharkovsky's cycle coexistence theorem. A simple non-directed graph proof which is especially suitable for a calculus course…

This note presents a simple proof of the characteristic function of Student's $t$-distribution. The method of proof, which involves finding a differential equation satisfied by the characteristic function, is applicable to many other…

Let $\Gamma$ be a Schottky semigroup in $\mathrm{SL}_2(\mathbf{Z})$, and for $q\in \mathbf N$, let $\Gamma(q):=\{\gamma\in \Gamma: \gamma= e \text{ (mod $q$)}\}$ be its congruence subsemigroup of level $q$. We prove the following uniform…

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

The purpose of this note is to give an accessible proof of Moliens Theorem in Invariant Theory, in the language of today's Linear Algebra and Group Theory, in order to prevent this beautiful theorem from being forgotten.

We prove a global effective membership result for polynomials on a non-reduced algebraic subvariety of $\C^N$. It can be seen as a global version of a recent local result of Sznajdman, generalizing the Brian\c{c}on-Skoda-Huneke theorem for…

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous…

The original proof of the Sharkovsky theorem is presented in full detail. The proof should be accessible to readers with basic Real Analysis background. Although nowadays there are several alternative proofs of this classical result, we…